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A comparison theorem for matrix limitation methods with applications

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Author(s): Rita Giuliano Antonini | Milan Paštéka

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 1;
Issue: 1;
Start page: 87;
Date: 2006;
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Keywords: Matrix limitation method | Toeplitz matrix | Riesz matrix | weighted density | asymptotic density | permutation of integers | Lévy group of permutations

ABSTRACT
A comparison Theorem for matrix limitation methods is proved and the following applications are given: paroindent - new results concerning the comparison between weighted densities generated by different weights; paroindent - new results concerning the comparison between weighted densities of a set $E\subseteq \mathbb N^*$ and those of its transformed set $\pi(E)$, where $\pi$ is a given injective function $\mathbb N^* \to \mathbb N^*$. In particular, a new class of permutations preserving the asymptotic density is identified.
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